It is virtually impossible to find a physiological function that does not actively involve single proteins or protein complexes at a certain stage. There is a huge gap in our knowledge of how protein structure relates to protein function or to cooperative mechanisms in macromolecular complexes, although these issues have been challenging scientists for many years. There is also great promise that understanding how systems such as proteins and protein complexes work, will impact the rational design of drugs and enzymes, and suggest better treatments for certain diseases. The intellectual merit of this project lies in the development of a novel framework to explore the conformational space of proteins and protein complexes. Our goal is to generate geometrically-distinct low energy conformations of the above systems. We will pursue the development of dimensionality reduction methods that are tailored to complex molecular systems and can be used to represent such systems compactly. Using those representations we will aggressively explore the conformational landscape of proteins, initially, and protein complexes, at a later stage. We believe that the tight coupling of dimensionality reduction and efficient search algorithms will result in a method that can reason about large systems with some probabilistic guarantees, a presently elusive goal. A distinguishing feature of our method is that we will modify and update our low-dimensional representations as the exploration of the conformational landscape progresses in order to best represent the considered system as it evolves. The output of our work can be used to study the possible shapes of a biomacromolecule and shed light on its function. As far as applications are concerned, we will first tackle problems that relate to molecular docking and computer-assisted drug design. In the long run, our goal is to study molecular machines and macromolecular assemblies in collaboration with experimentalists. The broader impact of the project is implemented through (a) interdisciplinary collaborations with the Texas Medical Center which will affect students in applied and computational mathematics, computer science, biology, and biochemistry, (b) training, mentoring and involvement in research activities of undergraduate, graduate and postdoctoral students, (c) course development at Rice University, (d) mentoring of women undergraduate students in computer science, and (e) participation in an NSF funded program of Rice University and the Houston Independent School District whose goal is to attract high school girls to fields where they are underrepresented.